A PTAS for the Sparsest Spanners Problem. Graphs of bounded local treewidth. Partial spanners. Idea of the algorithm. Apex-minor-free graphs. Page 3 ...

In this note, we resolve this open issue by showing that the sparsest t -spanner problem admits a polynomial time approximation scheme (PTAS) for every t ≥ 1.

Abstract. A t-spanner of a graph G is a spanning subgraph S in which the distance between every pair of vertices is at most t times their dis-.

The sparsest t -spanner problem asks to find, for a given graph G and an integer t, a t-spanner of G with the minimum number of edges. On general n-vertex ...

It is shown that the sparsest t-spanner problem admits the efficient polynomial time approximation scheme (EPTAS) for every t ≥ 1, and this result holds ...

We resolve this open issue by showing that the sparsest t-spanner problem admits the efficient polynomial time approximation scheme (EPTAS) for every t ≥ 1.

It is shown that the sparsest t-spanner problem admits the efficient polynomial time approximation scheme (EPTAS) for every t ≥ 1, and this result holds ...

We are interested in finding a sparsest -spanner. In the general setting, this problem is known to be NP-hard for all . For , the problem remains NP-hard for ...

An apex graph is a graph that can be made planar by the removal of a single vertex. We prove that the problem of finding a t-spanner of treewidth k is fixed ...

A PTAS for the sparsest spanners problem on apex-minor-free graphs. E. Ochmanski, J. Tyszkiewicz (Eds.), MFCS, Lecture Notes in Comput. Sci., vol. 5162 ...